adl1995
commented
6 years ago Inverse methods
Table 1
First 100K entries from GeographicLib dataset, i.e. the points randomly distributed on the ellipsoid.
| Method | Time (seconds) |
|---|---|
| Karney (order 1) | 0.855704 |
| Karney (order 2) | 0.866872 |
| Karney (order 3) | 0.866104 |
| Karney (order 4) | 0.878759 |
| Karney (order 5) | 0.894176 |
| Karney (order 6) | 0.921662 |
| Karney (order 7) | 0.950012 |
| Karney (order 8) | 0.986667 |
| Vincenty | 0.800606 |
| Thomas | 0.779644 |
| Andoyer | 0.775397 |
Table 2
First 200K entries from GeographicLib dataset, i.e. the points randomly distributed on the ellipsoid.
| Method | Time (seconds) |
|---|---|
| Karney (order 1) | 1.65711 |
| Karney (order 2) | 1.64782 |
| Karney (order 3) | 1.66457 |
| Karney (order 4) | 1.6728 |
| Karney (order 5) | 1.70661 |
| Karney (order 6) | 1.7836 |
| Karney (order 7) | 1.81258 |
| Karney (order 8) | 1.87114 |
| Vincenty | 1.54708 |
| Thomas | 1.56293 |
| Andoyer | 1.49774 |
Table 3
For 1e6 iterations. Comparison is done for the following input:
lon1=0., lat1=47.565626644319, lon2=0.010825815107066166, lat2=47.563010432984462575| Method | Distance | Azimuth | Reverse azimuth | Time (seconds) |
|---|---|---|---|---|
| Karney (order 1) | 865.0312267 | 109.6451634 | 109.6531532 | 1.172777374 |
| Karney (order 2) | 865.0302901 | 109.6451888 | 109.6531786 | 0.967596135 |
| Karney (order 3) | 865.0302906 | 109.6451888 | 109.6531786 | 0.968770456 |
| Karney (order 4) | 865.0302906 | 109.6451888 | 109.6531786 | 1.070992266 |
| Karney (order 5) | 865.0302906 | 109.6451888 | 109.6531786 | 1.078476219 |
| Karney (order 6) | 865.0302906 | 109.6451888 | 109.6531786 | 1.270175515 |
| Karney (order 7) | 865.0302906 | 109.6451888 | 109.6531786 | 1.334728774 |
| Karney (order 8) | 865.0302906 | 109.6451888 | 109.6531786 | 1.607816596 |
| Vincenty | 865.0302905 | 109.6451887 | 109.6531786 | 0.660409948 |
| Thomas | 865.0302877 | 109.6451889 | 109.6531787 | 0.679921994 |
| Andoyer | 865.0293549 | 109.6453179 | 109.6533078 | 0.481107833 |
@vissarion, @awulkiew - I think Karney's inverse method still needs to be further optimized. I will try to do so in the next days. If you have time, please review the code in #500.
Pranay711
Listed below are some performance benchmarks for the following methods:
Compiler used: g++ (version 7.2.0) Optimization level: O3
The execution times are calculated using the Boost Chrono library. I created a separate
.cppfile for each method, otherwise, I was getting similar execution times when all methods were placed in a single file. The code for a single file is available on GitHub. I used this Makefile for compiling all.cppfiles. The dataset associated with GeographicLib is used (https://zenodo.org/record/32156).Direct methods
Table 1
First 100K entries, i.e. the points randomly distributed on the ellipsoid.
Table 2
First 200K entries, i.e. the points randomly distributed on the ellipsoid.
Table 3
For
1e6iterations. Comparison is done for the following input: